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Automatic sequences and the link with number theory and algebraicity in positive characteristics

Abstract

We will give an introduction to automatic sequences and the link with number theory and algebraicity in positive characteristics. We will aboard the following topics:


1. Definition and Examples
We give classical examples of automatic sequences that arise naturally from
the study of various problems in different domains of mathematics.
We then give the definition via automata. We state and prove
Kleene's Theorem which asserts that every regular language is accepted by some deterministic finite automaton and vice versa.
2. Basic Properties
We give basic properties of automatic sequences, including two Theorems

of Cobham, the Pumping Lemma, and closure properties.


Schedule:

16:20-18:10, Apr 20,  22, 27, 29 and May 6, 11